Hmmm. It could be the belt tensioner, or one of the components that get turned by the belt. This evening I'll temporarily remove the serpentine belt, run the engine for less than 1 minute, listen for the noises, replace the serpentine belt, and report back here.

I forgot to mention none of the idiot lights are coming on, which is a good thing.

I briefly searched the SaturnFans ION forums where the Ecotec engines are also used. It seems the Ecotec engines can be a bit noisy; are not uncommon; they get louder with age; and sometimes the noises are due to lifters, injectors, faulty oil filters, for 5-speed manual transmissions a heat shield under the exhaust manifold, and maybe oil issues.